Algebraic and Differential Topology of Robust Stability

Algebraic and Differential Topology of Robust Stability

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In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential topology from an application-oriented point of view. It is suitable for graduate students in engineering and/or applied mathematics, and academic more

Product details

  • Hardback | 624 pages
  • 163.1 x 240.8 x 39.6mm | 1,088.63g
  • Oxford University Press Inc
  • New York, United States
  • English
  • New.
  • numerous line figures
  • 0195093011
  • 9780195093018

Review quote

"The opening sentence of the monograph reads as follows: 'In this book, two seemingly unrelated fields of intellectual endeavor--algebraic/differential topology and robust control--are brought together.' Indeed, there are probably just a few control engineers who are familiar with the modern concepts of algebraic and differential topology; others need strong motivation to learn these disciplines. The book under review attempts to convince experts in robustness analysis to do this and to provide the needed material to learn. . . . The book consists of 7 parts, which contain 26 chapters and 4 appendices. . . . [T]his book is a serious attempt to develop new approaches to robust stability. It will inspire research in control based on modern mathematics."--Mathematical Reviewsshow more

Table of contents

I. SIMPLICIAL APPROXIMATION AND ALGORITHMS ; 1. Prologue ; 2. Robust Multivariable Nyquist Criterion ; 3. A Basic Topological Problem ; 4. Simplicial Approximation ; 5. Cartesian Product of Uncertainties ; 6. Computational Geometry ; 7. Piecewise Linear Nyquist Map ; 8. Game of Hex Algorithm ; 9. Simplicial Algorithms ; II. HOMOLOGY OF ROBUST STABILITY ; 10. Homology of Uncertainty and Other Spaces ; 11. Homology of Crossover ; 12. Cohomology ; 13. Twisted Cartesian Product of Uncertainties ; 14. Spectral Sequence of Nyquist Map ; III. HOMOTOPY OF ROBUST STABILITY ; 15. Homotopy Groups and Sequences ; 16. Obstruction to Extending Nyquist Map ; 17. Homotopy Classification of Nyquist Maps ; 18. Brouwer Degree of Nyquist Map ; 19. Homotopy of Matrix Return Difference Map ; 20. K-Theory of Robust Stabilization ; IV. DIFFERENTIAL TOPOLOGY OF ROBUST STABILITY ; 21. Compact Differentiable Uncertainty Manifolds ; 22. Singularity Over Stratified Uncertainty Space ; 23. Structural Stability of Crossover ; V. ALGEBRAIC GEOMETRY OF CROSSOVER ; 24. Geometry of Crossover ; 25. Geopmetry of Stability Boundary ; Epilogue ; Appendicesshow more